$prod_i V_i$ is also a sub space of $B(H,K)$
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Suppose $V_i$ are subspaces of $B(H_i,K_i)$. Is it true that $prod_i V_i$ is also a sub space of $B(H,K)$ for some appropriate $H$ and $K$?
I think we need to take $H$ and $K$ to be direct product of $H_i$ and $K_i$ respectively but I am not sure. Can somebody help me?
linear-algebra functional-analysis operator-theory hilbert-spaces banach-spaces
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
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add a comment |
$begingroup$
Suppose $V_i$ are subspaces of $B(H_i,K_i)$. Is it true that $prod_i V_i$ is also a sub space of $B(H,K)$ for some appropriate $H$ and $K$?
I think we need to take $H$ and $K$ to be direct product of $H_i$ and $K_i$ respectively but I am not sure. Can somebody help me?
linear-algebra functional-analysis operator-theory hilbert-spaces banach-spaces
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
$endgroup$
$begingroup$
What type of spaces are $H_i, K_i$? Normed? If there is only finitely many of them the answer is true. Otherwise, there are different ways to define the norm of their direct sum (e.g $ell _1$, $ell _infty$ are different). And I am not sure what you mean.
$endgroup$
– pitariver
Jan 24 at 6:39
add a comment |
$begingroup$
Suppose $V_i$ are subspaces of $B(H_i,K_i)$. Is it true that $prod_i V_i$ is also a sub space of $B(H,K)$ for some appropriate $H$ and $K$?
I think we need to take $H$ and $K$ to be direct product of $H_i$ and $K_i$ respectively but I am not sure. Can somebody help me?
linear-algebra functional-analysis operator-theory hilbert-spaces banach-spaces
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
$endgroup$
Suppose $V_i$ are subspaces of $B(H_i,K_i)$. Is it true that $prod_i V_i$ is also a sub space of $B(H,K)$ for some appropriate $H$ and $K$?
I think we need to take $H$ and $K$ to be direct product of $H_i$ and $K_i$ respectively but I am not sure. Can somebody help me?
linear-algebra functional-analysis operator-theory hilbert-spaces banach-spaces
linear-algebra functional-analysis operator-theory hilbert-spaces banach-spaces
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
asked Jan 24 at 3:43
Math LoverMath Lover
1,004315
1,004315
$begingroup$
What type of spaces are $H_i, K_i$? Normed? If there is only finitely many of them the answer is true. Otherwise, there are different ways to define the norm of their direct sum (e.g $ell _1$, $ell _infty$ are different). And I am not sure what you mean.
$endgroup$
– pitariver
Jan 24 at 6:39
add a comment |
$begingroup$
What type of spaces are $H_i, K_i$? Normed? If there is only finitely many of them the answer is true. Otherwise, there are different ways to define the norm of their direct sum (e.g $ell _1$, $ell _infty$ are different). And I am not sure what you mean.
$endgroup$
– pitariver
Jan 24 at 6:39
$begingroup$
What type of spaces are $H_i, K_i$? Normed? If there is only finitely many of them the answer is true. Otherwise, there are different ways to define the norm of their direct sum (e.g $ell _1$, $ell _infty$ are different). And I am not sure what you mean.
$endgroup$
– pitariver
Jan 24 at 6:39
$begingroup$
What type of spaces are $H_i, K_i$? Normed? If there is only finitely many of them the answer is true. Otherwise, there are different ways to define the norm of their direct sum (e.g $ell _1$, $ell _infty$ are different). And I am not sure what you mean.
$endgroup$
– pitariver
Jan 24 at 6:39
add a comment |
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p08yA,U1VKknu akF 66HY AfG,6T5B4 duDr,hq6hxFfJoUFuj33NNpdBVCuzBg 3NH3z3r
$begingroup$
What type of spaces are $H_i, K_i$? Normed? If there is only finitely many of them the answer is true. Otherwise, there are different ways to define the norm of their direct sum (e.g $ell _1$, $ell _infty$ are different). And I am not sure what you mean.
$endgroup$
– pitariver
Jan 24 at 6:39